Abstract: We propose a simple model of two coupled mesoscopic rings threaded bymagnetic flux which mimics a device for electron transmission in a controlledfashion. Within a tight binding formalism we work out exactly the conditionswhen a completely ballistic transmission can be triggered at any desiredposition of the Fermi level within a continuous range of energy. The switchingaction can be easily controlled by appropriately tuning the values of the fluxthrough the two rings. The general transmission across the ring system displaysinteresting features characterized by the appearance and collapse of Fanoresonances, and the suppression of the Aharonov-Bohm oscillations in severalcases. We report and analyze exact analytical results for a few such cases.

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